What Happens to the Fourier Transform When Functions Are Scaled and Shifted?

[gomes.]

If f(t) has the Fourier transform F(ω), what is the Fourier transform of the function g(t) =
f(3t) − f(4t + 7)? Use the shift property and time scaling property of the Fourier transform
to obtain your answer.


I have no idea how to start, please help, thanks..

 

[cepheid]

Well, there is a reason why the homework help posting template (the thing you deleted when you typed your post) asks you to list some of the relevant equations -- they often give you an idea of where to start. So let's do that:

What is the shift property of the Fourier transform? How might it be applied to the functions you have been given?

What is the time scaling property of the Fourier transform? How might it be applied to the functions you have been given?